POLARIZED LIGHT FROM DIFFERENT SOURCES. 255
efficients of vibration in the two streams respectively, c cos a, c' sin a will be the coefficients of the resolved parts in the direction of the vibrations transmitted by the second tourmaline. Hence we shall have, mixing together, two independent streams, in one of which the temporary intensity fluctuates between the limits (cąc cos2 a)2 -f (o cos a sin a)2 as the interval of retardation changes in passing from one point to another in the field of view. The temporary intensity of the other stream being (c' sin a)2, the intensity at different points will fluctuate between the limits
m (c2 ą 2c2 cos2 a + c2 cos2 a) + m (c' sin a)2.
It is needless to take account of the absorption which takes place even on the pencils which the tourmalines do transmit, because it affects both pencils equally. Since m (c2) = Tit (c'2) = 1, we have for the limits of fluctuation of the intensity 2 + 2 cos2 a. When a = 0 these limits become 4 and 0, and the interference is perfect. When a = 90° the limits coalesce, becoming each equal to 2, and there are no fringes. As a increases from 0 to 90°, the superior limit continually decreases, and the inferior increases, and consequently the fringes become fainter and fainter.
21. It is a well-known law of interference that if two rays
of common light from the same source be polarized in rect- ||
angular planes, and afterwards be brought to the same plane of polarization, or in other words, analyzed so as to retain only light polarized in a particular plane, they will not interfere, but if the light be primitively polarized in one plane they will interfere. This law seems to have presented a difficulty to some, because, it would be argued, the most general kind of vibrations are elliptic, so that we must suppose the vibrations of the ether in the case of common light to be of this kind; and yet the phenomena of interference are exhibited perfectly well if the light be at first elliptically polarized instead of plane-polarized. For my own part, I never could see the difficulty, but on the other hand it seems to me that it would be an immense difficulty were the law anything else than what it is. For, if we consider the rectangular components of the vibrations which make up common light, these components being measured along any two rectangular axes perpendicular to the ray, we must suppose them to be independent of each other, or at least to